This seems like a problem with the temporary legal approval and not a genuine response to the question. In the US, parents accused of abuse are denied all parental privilege/responsibility at the beginning of the accusation until it is proven that the parent was innocent.

If your argument is that this regulation is fine as long as all other regulations are infallibly drafted and implemented, that only works until the other regulations are fallibly drafted and implemented. But fallible regulations are the rule rather than the exception.

Battered spouses frequently run away without notifying authorities, because leaving gets them out of the situation whereas contacting authorities extends and inflames the conflict.

And, because everything is a trade off, if you pass a law which is highly protective of victims then the abuser can file a false abuse complaint against the victim, then kidnap the children and deny the victim all access to their children until the fraudulent abuse complaint is dismissed.

Parental alienation is a thing. If the mother was making it up you'd be denying the child's right to a family life with its father, and the father's right to a family life with his child.

I was just stating how it works in the US. My mother was accused by neighbors when I was a child (certainly a much weaker tie than parental). I was taken away by the state immediately while they investigated. The claim was determined to be founded and the state took permanent custody.